Multivariate inverse trinomial distribution as a Lagrangian probability model

The univariate inverse trinomial distribution is so named because its cumulant generating function (c.g.f.) is the inverse of the c.g.f. of a trinomial distribution. The inverse trinomial distribution, which includes the inverse binomial and negative binomial distributions, is derivable from the Lagrangian expansion. The present paper pertains to the definition of the bivariate and multivariate inverse trinomial distributions through Lagrangian probability distributions. A multivariate inverse binomial distribution, generated by the method of reduction, converges to a multivariate inverse Gaussian distribution as a limiting form.